153 METHODVS VNIVERSALIS 



I. 2. 3- 4- 5- <5. 7- ^ 

 conftante. Siimma ergo feriei a-\-{,a-\-b)-\-{a-\'0.b)-\ 



-i-A; erit 1=,-^+ f-+-T\- 76 4-^5 -.7 — 16^-| 



ntque fumma feriei a- ~\-[a-\-by-\-{a-\-2.by 



Quae expreffiones fimiies funt eis, quas pro fummis po-r 

 teftatum numerorum naturalium in fuperiori diflertatio- 

 ne dedi, atque ex iis quoque facile formantur. 



§. 6. Sit nunc ad alteram huius generis formulam 

 inueniendam feries a dato termino X , cuius index fit x 

 in infinitum vsque fummanda, haec fcilicet 



X x-^b, x-\-zb 



X -f- Y -I- 2 -j- etc. infinitum — S. 

 In fumma ergo S fi pro x fcribatur x-\-b prodibit S — X, 

 ent adeo X = -77^^ - ^775^, -rTTdlT- " ^tc. vnde vt fu- 

 pra reperietur S — -/— -f- — -^yrTT.-d^^H-T^TTTj:^^:? 



1 .2 7<sdx* ' 1.2.3. p.iod*:'' 1 .2.3 - I i.edx' 



69l6''d"X - 35&'^d'^X , 36.76'Sd'5X 



J.2 3 I3.2I0dx" 1.2.3 - IJ. zdx'^ I 1.2.3 17. 30^«** 



— ,.2.3 .,., .9Td7^ H- etc. Lui formulae tanta con- 



ftans efl: adiicienda vt fiat S ~ o , fi ponatur .v ~ cvi ; 

 fi enim terminus X iam fuerit infinitefimus feu vltimus 

 in ferie , fumma debet efle euanefcens , fi quidem feries 

 finitam habeat fummam, pro quo cafu haec formiUa 

 eft accommodata. 



§. 7. Qiio vfus huius formulae appareat,. fit X— ^, 

 feu ifta feries ii-t-(-irq::^*-l-(3^^4&j*"~i- etc. in infinitum 



fum- 



